pseudo-wild numbers

[N. J. A. Sloane]

The following is an attempt at producing a sequence
which behaves like the Wild Numbers described by Enoch Haga
in his recent posting.  The idea is to find a map f from
rationals to rationals that occasionally produces an integer.
One starts at n = n/1, and iterates f until an integer is reached.
That integer is a(n).  If no integer is reached,
a(n) is defined to be zero.

%I A058971
%S A058971 3,2,6,3,3,4,10,87,6,6,9,7,6,6,87,9,6,10,7,8,9,12,9,15,12,10,16,15,
%T A058971 9,16,12,12,15,12,87,19,15,14,19,21,12,22,14,13,18,24,34,19,12,18
%N A058971 For a rational number p/q let f(p/q) = sum of divisors of p+q divided
 by number of divisors of p+q; a(n) is obtained by iterating f, starting at n/1,
 until an integer is reached, or if no integer is ever reached then a(n) = 0.
%O A058971 1,1
%K A058971 nonn,easy,more
%p A058971 with(numtheory); f:=proc(n) if whattype(n) = integer then sigma(n+1)/
sigma[0](n+1) else sigma(numer(n)+denom(n))/sigma[0](numer(n)+denom(n)); fi; end
;
%A A058971 njas, Jan 14 2001
%e A058971 1 -> (1+2)/2 = 3/2 -> (1+5)/2 = 3, so a(1) = 3.


Obviously many similar examples could be constructed.
Perhaps it will be possible to find one that comes
close to matching A058883, which is supposed to have
this kind of definition.

NJAS